1. Field of the Invention
This invention relates to magnetically coupled resonators, and more particularly to their use as narrow band filters having a high-loaded Q (quality factor) for increased selectivity, low insertion loss and improved out-of-band rejection for advantageous application in high frequency (HF), very high frequency (VHF) and ultra high frequency (UHF) bands, but which are simple and inexpensive to manufacture with a high degree of repeatable accuracy.
2. Background of the Related Art
The processing of broadband multi-carrier signals presents a particularly rigorous and stringent context for signal processing circuitry such as filters. The base-band television signal for example, which has a bandwidth on the order of about 5-6 MHz, is typically mixed with (to modulate) an RF (radio frequency) carrier signal in the range of 50 to 1000 MHz or greater, to achieve frequency division multiplexing (FDM). Applications which require the processing of broadband signals such as the broadcast and reception of television signals can present situations which require filters to pass only a small fraction of the total bandwidth (those frequencies fall within the pass band), while rejecting the rest of the frequencies over the total bandwidth (those falling within the stop-band). This is accomplished using a narrow band-pass filter.
Noise and image signals, as well as various undesired spurious signals, can be injected or generated at various points in processing, and thus band-pass filters are often called upon to reject (i.e. attenuate) out-of-band signals to significantly low levels, depending upon the sensitivity of the application. For example, even signals attenuated up to 60 dB can still be seen in received video transmissions. Thus, it is often critically important that any signals present other than the base-band signal modulated on the desired carrier be sufficiently attenuated. This often requires band-pass filters to be very selective (i.e. ideally passing only that fraction of the total bandwidth that contains the base-band signal of interest), with little or no loss of energy in the pass-band (i.e. low insertion loss), while meeting and maintaining the requisite measure of attenuation for all other frequencies in the stop-band. Moreover, because the fraction of the total bandwidth occupied by base band signals in broadband applications are so small relatively speaking (on the order of 1-2%), such filters must produce the requisite frequency response with a high degree of accuracy and must maintain that response over time (i.e. the response should not drift). Further, they must be relatively immune to RF noise from external sources, as well as from coupling between their own components. Finally, it is always desirable that the filters be inexpensive, and easy to manufacture with a high degree of repeatable accuracy.
There are several known techniques for implementing band-pass filters. As previously discussed, the Q value of a filter indicates its selectivity; a filter's selectivity is defined by how quickly the filter's response transitions from the pass band to the stop band. The higher the Q of a filter, the steeper the roll-off from pass band frequencies to stop band frequencies. Because the input and output loading of a filter affects its Q, a more useful and practical measure is its "in-circuit" or loaded Q (i.e. Q.sub.L). The Q.sub.L of a filter is roughly equal to the reciprocal of the fractional bandwidth of its frequency response, which is typically measured between the points on the response curve that are 3 dB below the peak of the response (i.e. the half-power points of the response). Thus, the Q.sub.L of a filter passing a 1-% fractional bandwidth is roughly 100. Narrow pass band filters for broadband signal processing applications often require a high value of Q.sub.L while exhibiting low insertion loss (i.e. the amplitude of signals in the pass band should not be significantly attenuated), and attenuation off signals in the stop-band should meet the requirements of the applications.
One known technique for implementing band-pass filters involves the use of lumped LC components to produce classical filters based on the technique of low-pass to band-pass transformation. Several variations of topologies can be synthesized for producing desired band-pass filter responses. The shortcomings of such filters are numerous for purposes of processing broadband signals in the VHF and UHF bands, the most serious of which is that the lumped components (particularly the coil inductors) are highly susceptible to parasitic effects at frequencies much above 100 MHz. Moreover, several stages of circuit components must be cascaded together to achieve the complexity of transfer function requisite for a high value of Q.sub.L. Thus, such filters take up valuable space and make their cost of manufacture relatively high.
Another known technique for implementing filters employs helical resonators. Filters employing helical resonators are magnetically and/or capacitively coupled and are capable of producing a response with the high Q.sub.L and low insertion loss requisite for many broadband signal-processing applications. They are not, however, suitable for frequencies much below 150 MHz, because very large inductor values would be required for the resonators below that frequency. Such inductors are impractical or impossible to construct. Moreover, even at higher frequencies they are rather large mechanical structures (they require shielding both for proper operation and to reduce susceptibility to RF noise), which makes them relatively expensive to manufacture (even in high volumes). They also are highly susceptible to environmental shock and drift, and they typically require an adjustment in value during the manufacturing process to make sure that they resonate accurately at the proper frequency.
Yet another known technique for building band-pass filters employs magnetically and/or capacitively coupled dielectric resonators, implemented either as cylindrical coaxial transmission lines, or as printed strip transmission lines sandwiched in between two ground plane shields. These resonators are short-circuited transmission lines, and as such are exploited for their ability to resonate at a particular frequency as a function of their length relative to the wavelength of the transmitted input signal (the length of the line is typically .lambda./4 for the wavelength .lambda. of the resonant frequency). Such resonators are capable of producing high Q.sub.L values to achieve responses having the fractional bandwidth characteristic requisite for many broadband signal-processing applications (i.e. 1-2%). Because the trace length increases as the desired resonant frequency decreases, however, such resonators are not suitable for anything other than UHF (i.e. between about 400 MHz and several GHz). They become cost prohibitive for HF and VHF applications because transmission line lengths increase to a prohibitive size. Moreover, their length must also be trimmed at production to ensure that they resonate at the requisite frequency.
Another well-known circuit topology for producing a band-pass filter response is that of the magnetically coupled double-tuned resonant circuit. Band-pass filters so implemented are the least expensive to manufactured relative to the other various prior art techniques discussed herein (they can be manufactured for a few cents each). Implementations of such filters heretofore known have been unable to achieve the large Q.sub.L values necessary to produce responses having small fractional bandwidths and low insertion loss requisite of many applications such as broadband signal processing (they have typically achieved no better than about 15% fractional bandwidth or greater). The reasons for their shortcomings in such applications will be apparent to those of skill in the art in view of the following discussion.
The generic topology of a series double-tuned circuit 10 is illustrated in FIG. 1a, and that of a parallel double-tuned circuit 100 is illustrated in FIG. 1b. The series tuned circuit has an input resonator circuit 12 that is magnetically coupled to an output resonator circuit 14. Likewise, the parallel tuned circuit 100 has an input resonator circuit 120 magnetically coupled to an output resonator circuit 140. The input resonators 12, 120 are coupled to an input source modeled by sources V.sub.S 18, 180 and associated source impedances R.sub.S 16 and 160 respectively. The output resonators 14, 140 are coupled to an output load impedance modeled by resistor R.sub.L 15, 150 respectively.
The input and output resonators 12, 14 of the series tuned circuit 10 are formed as a series connection between lumped series capacitors C.sub.S1 and C.sub.S2 13 respectively, and inductors L.sub.1 17 and L.sub.2 19 respectively. The two series tuned resonators 12, 14 and the two parallel tuned resonators 120, 140 are magnetically coupled as a function of the physical proximity between their inductors, whereby a mutual inductance M 21 is created. M=kL.sub.1 +L .multidot.L.sub.2 +L , where k is the coupling coefficient which has a value commensurate with the geometry and physical proximity (and thus reflects the percentage of total coupling) between the two resonators. The closer in proximity the two inductors 17, 19 or 170, 190 are, the greater the value of k and therefore the greater the mutual inductance between the resonators; likewise, the further they are apart, the lower the degree of coupling and thus the lower the value of k.
The parallel double-tuned circuit 100 is the theoretical dual of the series double-tuned circuit 10, and thus operates quite similarly. The resonators 120, 140 of the parallel tuned circuit 100 are formed as a parallel connection between lumped capacitors C.sub.P1 110 and C.sub.P2 130, and inductors L.sub.1 170 and L.sub.2 190 respectively. The parallel tuned resonators 120, 140 are also magnetically coupled as a function of the physical proximity between their inductors, whereby a mutual inductance M 210 is created. The mutual inductance of the parallel tuned circuit is given by the same equation, M=kL.sub.1 +L .multidot.L.sub.2 +L , with its value of k dictated by the same considerations.
FIG. 2 illustrates three typical responses of a double-tuned resonant circuit (either series or parallel), for different values of the coupling coefficient k. Response 22 is obtained when the two resonators are critically coupled, which is the point at which the tuned resonator exhibits minimum insertion loss with average selectivity at the resonant frequency. Response 24 illustrates the response of the double-tuned resonators 10 and 100, when their input, output resonators are under-coupled. This occurs for values of k approaching zero. As the resonators are moved further apart, the value of its QL increases (the fractional bandwidth decreases) but the insertion loss also increases, which is not desirable. Response 26 occurs when the two inductors are so close together they become over-coupled (i.e. k approaches a value of 1). Response 26 is characterized by two maxima on either side of the resonant frequency, and the circuit exhibits its lowest Q.sub.L value (and thus its largest fractional bandwidth). From these responses, it can be seen that there is a tradeoff, for this type of filter, between the maximum attainable Q.sub.L value and insertion loss as a function of the coupling.
The Q.sub.L for a series tuned circuit is roughly determined as the reactance X of the tuned circuit network at the resonant frequency, divided by the load or source impedance coupled to it. Thus, Q.sub.L for the output resonator ##EQU1##
Thus, for a given resonant frequency w.sub.o, one could increase the Q.sub.L by increasing the value of L.sub.2. (Of course, to increase the overall Q.sub.L for the double-tuned resonator, one would do the same for the input resonator 12 by increasing the value of L.sub.1 as well). The problem with this approach is that there are practical limitations on the size of the inductors L.sub.1, L.sub.2 that can be manufactured and implemented at a reasonable cost. Moreover, as the values of L.sub.1, L.sub.2 are increased, the parasitic shunt capacitance associated with a lumped value inductor (typically a coil) degrades the frequency response of the filter at frequencies above 200 MHz. Finally, because the resonant frequency is determined by the equation ##EQU2##
(for the output resonator 14), the value of C.sub.S2 must be reduced commensurately to maintain the value of w.sub.o. There are also practical limitations on how small C.sub.S2 can be built accurately.
FIG. 3 illustrates the series double-tuned circuit 10 of FIG. 1 with values for k, C.sub.S1 11 and C.sub.S2 13, and L.sub.1 17 and L.sub.2 19, designed to push the value of Q.sub.L for the circuit at a resonant frequency of 400 MHz. FIGS. 4a and 4b show the simulated response for the circuit 30 having the indicated component values as shown in FIG. 3. The pairs of values across the bottom of FIGS. 4a and 4b indicate the frequency (in MHz) and attenuation (in dB) values for the points 1-4 as indicated on the response curve. The response as shown in the scale provided in FIG. 4a illustrates the unacceptable performance of the filter at high frequencies for television signal processing applications. The smaller scale provided by FIG. 4b shows the 3 dB fractional bandwidth to be about 16% (and thus the approximate value of Q.sub.L is 6.25). As previously discussed, this is unacceptable for many broadband signal processing applications.
The Q.sub.L for a parallel tuned circuit is roughly determined as the admittance of the network at the resonant frequency, multiplied by the load or source impedance coupled to it. Thus, Q.sub.L for the parallel tuned output resonator 140 is.congruent.w.sub.o.multidot.C.sub.P2.multidot.R.sub.L. Thus, it can be seen that to increase Q.sub.L for the parallel tuned output resonator, one could increase the value of C.sub.P2 and R.sub.L. R.sub.L can't be increased much above 100 ohms, as the signal would tend to be shunted to ground through parasitic shunt elements. Increasing C.sub.P2 requires that L.sub.2 be made very small. To manufacture lumped inductors on the order of 5 nH with acceptable accuracy is very difficult, as such inductors are very sensitive to geometric variation, especially longitudinally. Further more, obtaining and maintaining proper coupling between such small coils on a repeatable basis is nearly impossible, primarily due to high sensitivity of the coupling coefficient to dimensional variations of a small gap between the two coupled coils (because the coils must be dimensionally small for small inductance values, the gap between them must also be small to achieve the desired coupling). The requisite small gap magnifies sensitivity to small dimensional variations. Such component and dimensional variations cannot be tolerated when fractional bandwidths on the order of 1% are required.
FIG. 5 illustrates the parallel double-tuned circuit 100 of FIG. 1 with values for k, C.sub.P1 110 and C.sub.P2 130, and L.sub.1 170/L.sub.2 190, with an L to C ratio designed to push the value of Q.sub.L for the circuit at a resonant frequency of 400 MHz. FIGS. 6a and 6b show the simulated response for the circuit 50 having the indicated component values as shown in FIG. 3. The pairs of values across the bottom of FIGS. 6a and 6b indicate the frequency (in MHz) and attenuation (in dB) values for the points 1-4 as indicated on the response curve. The response as shown in the scale provided in FIG. 6a illustrates the unacceptable performance of the filter in the stop-band, even though it operates more symmetrically at high frequencies relative to the series tuned circuit 30 of FIG. 3. Even though the coils values used in this example of the prior art are being pushed to the limit, the bandwidth of this filter is still not narrow enough for many applications. The smaller scale provided by FIG. 6b shows the 3 dB fractional bandwidth to be about 15.5% (and thus the approximate value of Q.sub.L is 6.45. As previously discussed, this is unacceptable for many broadband signal processing applications that require fractional bandwidths of 1 to 2% (i.e. Q.sub.L values in the 50 to 100 range).
Thus, those of skill in the art will recognize the need for band-pass filter circuits that provide characteristics required for many broadband signal processing applications over bandwidths spanning about 50 to 1000 MHz. Those characteristics are namely high Q.sub.L values to provide high selectivity and therefore small fractional bandwidths, high attenuation in the stop-band, low insertion loss in the pass-band but which can be manufactured as cheaply and repeatably as the tuned resonator circuits of the prior art.